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3604 IEEE TRANSACTIONS ON MAGNETICS, VOL. 37, NO. 5, SEPTEMBER 2001 Advanced Electromagnetic Field Visualization Using the Virtual Reality Modeling Language Standard Michael Bartsch, Markus Clemens, Tobias Hippler, and Thomas Weiland Abstract—The Virtual Reality Modeling Language (VRML) is presented to be suited for the visualization of 3-D results of electromagnetic field simulations, here performed with the CAE program MAFIA. Based on shape primitives, it allows the mod- eling of transparent materials and arbitrary object coloration. Its object oriented approach allows the combination of contour and arrow plots with ease. The VRML interpolator mechanism is used to include animated arrow plots and moving charged particles. Index Terms—Software engineering, virtual reality, visualiza- tion, VRML. I. INTRODUCTION M AFIA is based on the Finite Integration (FI) method [1], a proven consistent discretization scheme for Maxwell’s equations in integral form. The FI method allows the simulation of realistic 3-D electromagnetic field problems with up to several million degrees of freedom on todays PCs or workstations. The advanced graphic representation of the results is a basic task of CAE analysis. MAFIA’s postprocessor enables a suitable graphic preparation of the calculated results as arrow-, contour- or isosurface plots [2]. Before rendering, the graphic information is stored as triangulated surfaces in a so called graphic-pipeline. This interface enables an easy data exchange to advanced graphic systems which allow a fast and interactive visualization. For this the Virtual Reality Modeling Language (VRML) [3] is used, which has been implemented to all common internet browsers. II. THE VIRTUAL REALITY MODELING LANGUAGE The first VRML 1.0 specification originates from the proto- type 3-D web interface “Labyrinth,” developed by Mark Peske and Tony Parisi in 1994. The Open Inventor ASCII File Format from Silicon Graphics Inc. is the basis of VRML 1.0. This first release of VRML sup- ports the complete description and manipulation of 3-D static scenes. The VRML Architecture Group (VAG) formed in 1995 issues the RFP (Request For Proposal) for VRML 2.0, which was officially released at the Siggraph 96 conference. In 1997 VRML 2.0 was stated as an International Standard: VRML97 Manuscript received June 5, 2000. M. Bartsch and T. Hippler are with the Computer Simulation Technology GmbH, Büdingerstr. 2a, 64289 Darmstadt, Germany (e-mail: [email protected]). M. Clemens and T. Weiland are with the Darmstadt University of Technology, FB18 Elektrotechnik und Informationstechnik, Fachgebiet Theorie Elektromagnetischer Felder, 64289 Darmstadt, Germany (e-mail: clemens/[email protected]). Publisher Item Identifier S 0018-9464(01)07880-3. [4]. Now animation, viewpoint binding, texture animation, timers and scripting is supported, making advanced 3-D web content possible. In 1999 the Web3D Consortium joins the W3C to form X3D as the next generation VRML 2002 ISO standard, being fully compatible with VRML97 content and based on XML [5]. VRML is a scene graph-based 3-D system. All information that defines a 3-D scene is stored in so-called “nodes” of the graph. Most of the nodes have special purposes, like holding geometry data, appearance information or transformation rules. Each frame the graph is traversed and it’s nodes are processed. VRML includes an event oriented system which enables the nodes to interact with each other and with the user. Being a fully descriptive ASCII code language, VRML files can easily be pro- duced and edited by any text editor. III. FUNCTIONAL SPECIFICATION The postprocessing of numerical data from CAE calculations needs advanced visualization methods to interpret the results in a convenient way. In addition to the shapes of the modeled geometry vector fields, scalar fields, electron rays and moving particles have to be displayed. Depending on the kind of the physical quantity, different types of plots are known. Materials of the modeled geometry are visualized by different colors and transparency. Vector fields are usually represented by arrows or cones and their size represents the strength of the physical quantity. Scalar fields are visualized by iso shapes (3-D) or as contour plots (2-D) in cross sections of the geometry. Interactivity, like changing the viewing position, object trans- parency or the color spectrum gives the user the possibility to “explore” the scenes. As electromagnetic fields are propagating, EM-simulations often represent a dynamic process. Traveling waves should be represented by moving arrows, which requires the control over the animation speed and size of the arrows. Finally it should be possible to combine these different com- ponents into one scene. This way different aspects of different simulations can be combined into a new scene. IV. REALIZATION The VRML rendering of complex solid objects is easily done with the IndexedFaceSet node. It provides a data structure to ef- ficiently store triangle data and color information. This node is the most common building block of any VRML scene. Through a global naming mechanism it is possible to define and reuse any type of object, like geometry, shape or material. This enables the 0018–9464/01$10.00 © 2001 IEEE

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Page 1: Advanced electromagnetic field visualization using the virtual reality modeling language standard

3604 IEEE TRANSACTIONS ON MAGNETICS, VOL. 37, NO. 5, SEPTEMBER 2001

Advanced Electromagnetic Field Visualization Usingthe Virtual Reality Modeling Language Standard

Michael Bartsch, Markus Clemens, Tobias Hippler, and Thomas Weiland

Abstract—The Virtual Reality Modeling Language (VRML)is presented to be suited for the visualization of 3-D results ofelectromagnetic field simulations, here performed with the CAEprogram MAFIA. Based on shape primitives, it allows the mod-eling of transparent materials and arbitrary object coloration. Itsobject oriented approach allows the combination of contour andarrow plots with ease. The VRML interpolator mechanism is usedto include animated arrow plots and moving charged particles.

Index Terms—Software engineering, virtual reality, visualiza-tion, VRML.

I. INTRODUCTION

M AFIA is based on the Finite Integration (FI) method[1], a proven consistent discretization scheme for

Maxwell’s equations in integral form. The FI method allowsthe simulation of realistic 3-D electromagnetic field problemswith up to several million degrees of freedom on todays PCsor workstations. The advanced graphic representation of theresults is a basic task of CAE analysis. MAFIA’s postprocessorenables a suitable graphic preparation of the calculated resultsas arrow-, contour- or isosurface plots [2]. Before rendering,the graphic information is stored as triangulated surfaces in aso called graphic-pipeline. This interface enables an easy dataexchange to advanced graphic systems which allow a fast andinteractive visualization. For this the Virtual Reality ModelingLanguage (VRML) [3] is used, which has been implemented toall common internet browsers.

II. THE VIRTUAL REALITY MODELING LANGUAGE

The first VRML 1.0 specification originates from the proto-type 3-D web interface “Labyrinth,” developed by Mark Peskeand Tony Parisi in 1994.

The Open Inventor ASCII File Format from Silicon GraphicsInc. is the basis of VRML 1.0. This first release of VRML sup-ports the complete description and manipulation of 3-D staticscenes.

The VRML Architecture Group (VAG) formed in 1995issues the RFP (Request For Proposal) for VRML 2.0, whichwas officially released at the Siggraph 96 conference. In 1997VRML 2.0 was stated as an International Standard: VRML97

Manuscript received June 5, 2000.M. Bartsch and T. Hippler are with the Computer Simulation Technology

GmbH, Büdingerstr. 2a, 64289 Darmstadt, Germany (e-mail: [email protected]).M. Clemens and T. Weiland are with the Darmstadt University of

Technology, FB18 Elektrotechnik und Informationstechnik, FachgebietTheorie Elektromagnetischer Felder, 64289 Darmstadt, Germany (e-mail:clemens/[email protected]).

Publisher Item Identifier S 0018-9464(01)07880-3.

[4]. Now animation, viewpoint binding, texture animation,timers and scripting is supported, making advanced 3-D webcontent possible.

In 1999 the Web3D Consortium joins the W3C to form X3Das the next generation VRML 2002 ISO standard, being fullycompatible with VRML97 content and based on XML [5].

VRML is a scene graph-based 3-D system. All informationthat defines a 3-D scene is stored in so-called “nodes” of thegraph. Most of the nodes have special purposes, like holdinggeometry data, appearance information or transformation rules.Each frame the graph is traversed and it’s nodes are processed.VRML includes an event oriented system which enables thenodes to interact with each other and with the user. Being a fullydescriptive ASCII code language, VRML files can easily be pro-duced and edited by any text editor.

III. FUNCTIONAL SPECIFICATION

The postprocessing of numerical data from CAE calculationsneeds advanced visualization methods to interpret the resultsin a convenient way. In addition to the shapes of the modeledgeometry vector fields, scalar fields, electron rays and movingparticles have to be displayed.

Depending on the kind of the physical quantity, differenttypes of plots are known. Materials of the modeled geometryare visualized by different colors and transparency. Vectorfields are usually represented by arrows or cones and their sizerepresents the strength of the physical quantity. Scalar fieldsare visualized by iso shapes (3-D) or as contour plots (2-D) incross sections of the geometry.

Interactivity, like changing the viewing position, object trans-parency or the color spectrum gives the user the possibility to“explore” the scenes.

As electromagnetic fields are propagating, EM-simulationsoften represent a dynamic process. Traveling waves should berepresented by moving arrows, which requires the control overthe animation speed and size of the arrows.

Finally it should be possible to combine these different com-ponents into one scene. This way different aspects of differentsimulations can be combined into a new scene.

IV. REALIZATION

The VRML rendering of complex solid objects is easily donewith the IndexedFaceSet node. It provides a data structure to ef-ficiently store triangle data and color information. This node isthe most common building block of any VRML scene. Througha global naming mechanism it is possible to define and reuse anytype of object, like geometry, shape or material. This enables the

0018–9464/01$10.00 © 2001 IEEE

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BARTSCHet al.: ADVANCED ELECTROMAGNETIC FIELD VISUALIZATION USING THE VIRTUAL REALITY MODELING LANGUAGE STANDARD 3605

Fig. 1. The scene control enables the user to modify several attributes of the3-D objects, like transparency, shape color or the color spectrum for contourplots. The buttons on the right change the background color from black to white,traverse the scene graph to select objects, and hide the control.

creation of complex, but less memory consuming scenes. Fur-thermore new prototypes of graphical objects can be created.This means encapsulating visual appearance and behavior intoa new object class and defining an interface consisting of inputand output fields. This approach is similar to the so-called sub-classing in object oriented programming. These new prototypescan be used as new building blocks in any scene. The behaviorof objects is their ability to respond to events, like user interac-tion (mouse click) or the passing of time, with certain actions.These actions can be transformations or a change of attributes oreven the calling of user defined functions, which can be added tothe scene using JavaScript. Incorporating scripts is very impor-tant for a dynamic interactive scene. VRML’s JavaScript supportgives a very detailed control over the objects in the scene.

Every VRML node has an interface which is designed toexchange data and events with other nodes. Hence, building be-havior basically means routing one node’s output field to theother node’s input field, so that whenever the first node producesnew output, the other node is triggered to process the newly re-ceived data.

The MAFIA VRML export module supports static, dynamicand moving scenes. The output of the MAFIA graphicspipeline is directed immediately to the VRML converter.The extracted information contains a simple description ofthe scene consisting of triangles and macro elements (likearrows or particles) and its attributes. These attributes assignthe corresponding object type (material-shape, arrow-field,iso-surface or particle-field), the element geometry (triangle ormacro elements coordinates) and its static and time dependentproperties (color, transparency, size and orientation). Duringconversion the information is sorted, packed and classified byits object types. To minimize the size of the VRML file indexedaddressing of the triangle coordinates is used. Furthermoreredundant element definitions are removed.

The standard VRML browser functionality allows to look ata scene with arbitrary camera positions. To enhance this func-tionality, an additional scene control panel has been developed.It appears on a fixed location at the bottom of the scene. It isrealized as an independent 3-D object with complex scripts at-tached to it.

The implementation of the scene control panel massively usesthe VRML’s reuse and prototyping facilities. The sliders, thecolor selectors and the buttons are new VRML extensions cre-ated with the prototype mechanism.

By means of a special JavaScript, the user is able to pick acertain object from the scene. Once an object is selected, itsattributes, like color, transparency and size can be modifiedwith the scene control element. So any aspect of interest of the

(a)

(b)

Fig. 2. The electric field of the roof antenna taken from the car example shownbelow. The picture shows (a) the field with an interval [0;1] and (b) the field withan interval [0;0.5] mapped to a color spectrum.

visualized numeric data can easily be presented in a convenientand fitting way.

To omit unnecessary information from the VRML file, thecomplexity of the scene control depends on the individual scene.With regard to the present scene objects, only the necessarypanel elements are created.

VRML’s scripting facility [8] furthermore allows to bring an-imation effects and user interactivity into the scene. This enablesthe user to create dynamic, moving scenes or to add algorith-mical modifications. The Script node is used to define functionsand procedures in JavaScript.

Fig. 2 shows an example to the interactive modification of astatic scene. The shown pictures visualize the absolute valuesof the field strength of a radiating antenna as a contour plot ina cross section of the geometry. The scalar field values are nor-malized to the interval [0;1] and then mapped to a color spec-trum. To enable the examination of local extrema it is possibleto interactively adjust the interval boundaries of the spectrum,to get a finer color resolution.

The animation of dynamic scenes, like the propagation oftraveling waves—displayed by rotating arrows which are scaledby the field amplitude—is realized by taking several succes-sive (3-D) snapshots from the simulation program. During theVRML conversion the monitored orientation and size of everyarrow is analyzed to create a so called OrientationInterpolatorfor each element. While running the VRML movie-scene theseinterpolators calculate the arrow appearance in real-time. Thistechnique keeps all 3-D information and results in a small filesize.

The same technique is used to visualize moving particlestreams as they are calculated by the MAFIA PIC simulators.Here, PositionInterpolators [9] are used instead of Orientation-Interpolators to create moving objects.

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3606 IEEE TRANSACTIONS ON MAGNETICS, VOL. 37, NO. 5, SEPTEMBER 2001

Fig. 3. Field emission from a roof antenna at 1 Ghz. The magnetic and electricfield strength are shown as arrow and contour plot in a cross section of theantenna. VRML file size: 2.7 MB.

A key feature of the VRML translation is the option to com-bine different scene modules into a new scene. To achieve this,the translation process is performed in four steps:

1) Preprocessing: During this phase the work up of the dataof the CAE simulation program is performed. To ensurethe possible exchange of the data all geometric informa-tion is stored in world coordinates.

2) Generation of a VRML meta file: In this phase a meta-filecontaining a general information block and the basicVRML description of the scene is created.

3) VRML Scene Composition: One or more meta-files areselected to build a new scene.

4) VRML Scene Generation: The complete VRML filebased on one or more meta files is composed. Thenecessary script and control elements depending on thecontent and complexity of the scene are added.

The scene composition is performed interactively. Differentaspects of the simulation results can be presented in a singlescene. The examples give an overview about different simula-tions and its VRML results.

V. EXAMPLES

Three examples are presented here:

1) 3-D time-domain simulation of a roof antenna (Fig. 3);2) 3-D frequency-domain simulation of an eddy current

sensor (Fig. 4);3) 3-D thermodynamic simulation of an HF heating coil

(Fig. 5).Fig. 3 shows a car with a roof antenna, which is nowadays

very common for cellular phones to be used inside car in orderto avoid strong field intensities to be trapped in the drivers head[11].

A combined rendering of both electric (contours) and mag-netic fields (arrows) at a given 2-D plane right across the roof an-tenna is displayed. The outgoing propagating phenomenon canclearly be seen.

It is first calculated by the MAFIA time-domain solver withboth electric and magnetic fields being recorded at certain spe-cific time steps. The two numeric quantities are then representedas contour lines and arrows by the MAFIA postprocessor. The

Fig. 4. Eddy current sensor as used a contact free position sensor. The arrowsshow the magnetic field strength. The contour plot on the material surfacerepresents the absolute of the eddy currents. VRML file size 787 KB.

contours and arrows are independent of each other and can berendered separately. With the Scene-Composition function ofthe MAFIA VRML facility, these two objects can be combinedas easily as if you were laying them on top of each other in thephysical world. This also implies that it is possible to mergeany number of totally unrelated objects together, thus allowingan unlimited exercise of fancy creativity. The MAFIA VRMLauto-scaling facility always accommodates the user with themost suitable view.

Non-contact mechanic-electric conversion devices are widelyused in our daily life. Fig. 4 shows a 4 cm4 cm 4 cm me-chanical displacement sensor [10] which detects fine variationsof inductance with an external electronic circuit. Two indepen-dent sensors, which are uncoupled due to perpendicularity, areconstructed in one piece. The sensor on the left side is poweredby the smaller driving coil (10 kHz harmonic) while the left-most is a copper shielding ring. The inductance of the drivingcoil is almost linearly proportional to the distance between thecoil and the ring. In practice, the shielding ring is fixed whilethe coil is connected to a movable transmission rod. The deviceshown here is used as a clutch sensor in a car.

The object of study here is the calculation of the linear depen-dence of inductance on the coil-ring distance with the MAFIAfrequency-domain solver.

In Fig. 4, arrows represent magnetic field flux while theshaded contour area represents the absolute value of the eddycurrents on the surface of the yoke. The shielding effect of thering can clearly be seen. The four holes in the device are cutout to hold mounting screws.

In this plot, a total of three separate visualizations are com-bined: the geometry itself, the arrow-plot of the magnetic flux,and the contour-plot of the eddy currents.

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BARTSCHet al.: ADVANCED ELECTROMAGNETIC FIELD VISUALIZATION USING THE VIRTUAL REALITY MODELING LANGUAGE STANDARD 3607

(a)

(b)

Fig. 5. Heat simulation of a cavity’s inductive soldering. The temperaturedistribution on the device is shown as contour plot on the material surface. Thearrows represent the heat flux. VRML file size 478 KB.

HF heating for massive soldering finds a wide applicationin industry. Sometimes, it is difficult to control the solderingtemperature, for it directly relates to the power of the HF coiland its duration.

Fig. 5(a) shows a quarter copper cavity of two cells, whichis used in particle accelerators [12]. It is about 10 cm in diam-eter and 7 cm long (3.5 cm each cell). The two cells are sol-dered together by an inducted eddy current heating mechanism.The outer winded heating coil (not shown) is driven by a 7 kW10 kHz power. The melting point of the used melding filamentsis 782 C. To avoid misalignment of the structure, tempera-ture must be below 890C. In order to find out the dependence

of temperature on the power duration, a coupled simulation isperformed with the MAFIA frequency-domain solver, whichyields the lossy eddy current distribution, and the MAFIA ther-modynamic solver, using the eddy current losses as its heatingsource. Thus a transient temperature development can be ob-tained with a weak coupling of both processes.

Fig. 5(b) shows both temperature distribution (left, contourplot) and heat flow vector. The arrow direction clearly depictswhere the thermal energy flows. This is actually the sameVRML file with the cavity made transparent by the scenecontrol panel.

VI. CONCLUSION

This paper presents the application of the Virtual RealityModeling Language for the visualization of electromagneticfields. The software methodology is described to create spe-cialized VRML scenes which are fitted to be used for thevisualization of electromagnetic field simulations.

Being a complete 3-D description language, VRML is able toreproduce any 3-D scene without loss of details. Since VRMLis supported by most web browsers through plug-ins (e.g., theCosmoPlayer plug-in by Cosmo-Software [6]), the primary ben-efits are its platform independence and portability. Thus VRMLis an ideal tool for educational purposes and the worldwide pub-lishing of simulation results on the internet.

The VRML Standard will be fully included to the new X3Dstandard. X3D is supported by the W3C Consortium whose ded-icated mission is the development and improvement of 3-D webgraphics.

REFERENCES

[1] T. Weiland, “Time domain electromagnetic field computation with fi-nite difference methods,” inInt. J. Num. Mod.: ENDF, 1996, vol. 9, pp.295–319.

[2] M. Bartsch, T. Weiland, and M. Witting, “Generation of 3D isosurfacesby means of the marching cube algorithm,”IEEE Trans. Magn., 1996.

[3] VRML. Info., Technical Specification. [Online]. Available:www.vrml.org.

[4] History of VRML. [Online]. Available: http://www.vrml.org/about/his-toryofvrml.html.

[5] X3D.. [Online]. Available: http://www.vrml.org/fs_announce-ments.htm.

[6] CosmoSoftware.. [Online]. Available: http://www.cosmosoftware.com.[7] C. Marrin and B. Campbell,Teach Yourself VRML in 21 Days, First ed:

Sams.net Publishing, 1997, pp. 50–55.[8] , Teach Yourself VRML in 21 Days, First ed: Sams.net Publishing,

1997, pp. 161–179.[9] , Teach Yourself VRML in 21 Days, First ed: Sams.net Publishing,

1997, pp. 139–154.[10] P. Hahne and T. Weiland, “3D eddy current computation in frequency

domain regarding the displacement current,”IEEE Trans. Magn., vol.MA-28, no. 2, pp. 1801–1804, 1992.

[11] R. Ehmann, “Fernfeldberechnung und Gewinnung zeitharmonischerFeldaten aus Zeitbereichssimulationen,” Ph.D. dissertation, DarmstadtUniversity, D17, 1999. ISBN 3-8265-6677-7.

[12] M. Clemens, E. Gjonaj, P. Pinder, and T. Weiland, “Numerical simu-lation of coupled transient thermal and electromagnetic fields with theFI-method,”IEEE Trans. Magn., pp. 1448–1452, 2000.